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Oecologia DOI 10.1007/s00442-013-2646-3 COMMUNITY ECOLOGY - ORIGINAL RESEARCH Disturbance and trajectory of change in a stream fish community over four decades William J. Matthews • Edie Marsh-Matthews Robert C. Cashner • Frances Gelwick • Received: 24 April 2012 / Accepted: 15 March 2013 Ó Springer-Verlag Berlin Heidelberg 2013 Abstract Communities can change gradually or abruptly, and directionally (to an alternate state) or non-directionally. We briefly review the history of theoretical and empirical perspectives on community change, and propose a new framework for viewing temporal trajectories of communities in multivariate space. We used a stream fish dataset spanning 40 years (1969–2008) in southern Oklahoma, USA, emphasizing our own 1981–2008 collections which included well-documented, extreme drought and flood events, to assess dynamics of and environmental factors affecting the fish community. We evaluated the trajectory of the Brier Creek community in multivariate space relative to trajectories in 27 published studies, and for Brier Creek fish, tested Communicated by Jeff Shima. Electronic supplementary material The online version of this article (doi:10.1007/s00442-013-2646-3) contains supplementary material, which is available to authorized users. W. J. Matthews (&) E. Marsh-Matthews Department of Biology, University of Oklahoma, Norman, OK 73019, USA e-mail: [email protected] E. Marsh-Matthews Sam Noble Oklahoma Museum of Natural History, Norman, OK 73072, USA R. C. Cashner University of New Orleans, New Orleans, LA 70148, USA Present Address: R. C. Cashner 105 Continental Drive, Flat Rock, NC 28731, USA F. Gelwick Department of Wildlife and Fisheries Sciences, Texas A&M University, College Station, TX 77843-2258, USA hypotheses about gradual versus event-driven changes and persistence of shifts to alternate states. Most species were persistent, qualitatively, across the four decades, but varied widely in abundance, with some having unusually strong reproduction after extreme droughts. The community had an early period of relatively gradual and directional change, but greater displacement than predicted at random after two consecutive extreme droughts midway through the study (1998 and 2000). But, the community subsequently returned toward its former state in the last decade. This fish community is characterized by species that are tolerant of environmental extremes, and have life history traits that facilitate population recovery. The community appears ‘‘loosely stable’’ about a long-term average condition, but the impacts of the two consecutive droughts were substantial, and may foretell future dynamics of this or other communities in a changed global climate if disturbance events become more frequent or severe. Keywords Drought Flood Long-term change Oklahoma Succession vectors Introduction ‘‘How do communities change over time?’’ and ‘‘how do communities respond to disturbances?’’ are two of the long-standing, overarching questions in ecology, dating at least to Shelford (1911). The theoretical approaches that appeared in the middle of the last century (MacArthur 1955, 1960; Lewontin 1969; May 1973) for dynamics of communities in n-dimensional space provided a framework in which ecologists continue to view community dynamics. Holling (1973) emphasized the role of random events, the ability of a system to absorb perturbations or return to a 123 Oecologia previous state after disturbance, and the possibility for community change by ‘‘sudden steps.’’ Using long-term data for marine fouling communities, Sutherland (1974) emphasized responses to perturbations and recognized multiple stable points. Aggregating previous suggestions, Connell and Sousa (1983) defined community stability both quantitatively as ‘‘resistance’’ to change or ‘‘elasticity’’ after disturbance, and qualitatively as ‘‘persistence’’ of species in a community. More recently, based on long-term studies of prairie plant and animal communities, Collins (2000) contributed the concept that real-world communities may exist over time in a global, ‘‘loosely stable’’ equilibrium. Beginning in the 1970s, core questions on community dynamics were addressed by ecologists using multivariate approaches to describe temporal changes in real communities (Allen and Skagen 1973; Allen et al. 1977) visualized in ordination biplots as trajectories to track changes or identify multiple stable points. Austin (1977) subjectively described ‘‘reversals of trends’’ on ordination biplots of plant communities. Subsequent studies on many different communities also used trajectories in multivariate space to assess community stability (Bloom 1980; Santos and Bloom 1980; Hughes 1990; Vieira et al. 2004; Magalhães et al. 2007), identify alternative community states (Warwick et al. 2002; Daufresne et al. 2007), or detect changes after perturbation (Boulton et al. 1992; Adjeroud et al. 2009; Muehlbauer et al. 2011). These and other studies revealed a broad spectrum of community changes in response to various underlying mechanisms, with trajectory patterns including both smooth or ‘‘gradual’’ and abrupt or ‘‘saltatory’’ changes, and patterns of change that were either directional or non-directional (idiosyncratic). We propose that scenarios of community change can be visualized in a cross-classified framework (Fig. 1) in which a community could change: (1) by gradual steps or by saltatory changes; and (2) either (a) idiosyncratically, (b) directionally persistent, or (c) directionally but followed by return toward a previous state. See Smith (2012), Lake et al. (2007), or Mittlebach et al. (2006) for other hypothetical patterns related to community change or recovery from a stressor. First, in our scheme a community may be characterized by idiosyncratic changes (Drake 1991; Matthews and Marsh-Matthews 2006a), and lack an overall directional trajectory in multivariate space (Fig. 1a, d). A community characterized by gradual variation exhibits regular increments of change (Fig. 1a–c), with directional change, if any (Fig. 1b, c), that could result from a chronic ‘‘press’’ disturbance (Lake 2000), or from long-term turnover of species (Magurran and Henderson 2010). In contrast, a predominantly event-driven community (Fig. 1d–f) may show little change until ‘‘pulse’’ or ‘‘ramp’’ events (Lake 2000) or an experimental treatment (Muehlbauer et al. 2011) result in a relatively large, saltatory move (Sponseller et al. 123 2010). Regardless of the drivers, community changes may be directional (Collins 2000), diverging overall from the original state, or not. Saltatory changes may be directional (Fig. 1e, f), to an alternate community state (Scheffer and Carpenter 2003; Paine and Trimble 2004) differing markedly from the original structure. And after either gradual or eventdriven change to a new state (Fig. 1b, c, e, f), a community may subsequently return toward its previous condition (Fig. 1c, f) as exemplified by Eby et al. (2003) and Muehlbauer et al. (2011), or remain in a stable alternative state (Fig. 1b, e) as shown in Daufresne et al. (2007) and Rodriguez et al. (2003). A community may not exclusively fit either a gradual or an event-driven model, as real communities can show both gradual and rapid changes at various times (Warwick et al. 2002; Daufresne et al. 2007), and return toward a previous state can be partial (Gardner and Wear 2006) or complete (Muehlbauer et al. 2011). It is unlikely that any real-world community will conform precisely to any one of the six patterns we propose in Fig. 1, given sufficient time for disturbances of different magnitudes or random events affecting recruitment of species. But these patterns should provide a point from which to view long-term changes in natural communities, ask questions about underlying drivers, or help inform focused experiments on potential biotic (e.g., life history) or abiotic (environmental) drivers of change. As a first test for the generality of the hypothetical patterns (Fig. 1), we reviewed a total of 71 multivariate trajectories appearing in 27 published papers (ESM1) on a wide variety of taxa, not including the trajectory of the system (Brier Creek, Oklahoma, USA) that is the focus of this paper. All of the hypothetical trajectories in Fig. 1 were exhibited by at least some of the communities we reviewed. In 23 of the 71 trajectories there was at least one saltatory directional change, followed by recovery toward pre-change conditions (Fig. 1f). Another 19 exhibited at least one period of directional saltatory change but no return toward an earlier state (Fig. 1e). Thus, 42 of 71 (=59 %) of the trajectories showed at least one saltatory change. Five other trajectories had one or more saltatory changes, but no overall directional change in multivariate space (Fig. 1d). In the other 29 trajectories change was by gradual increments whether directional (15 cases; Fig. 1b) or not (six cases; Fig. 1a), or whether there was any pattern of return toward an earlier state (three cases; Fig. 1c). Thirty-four trajectories were directional without return, whereas 26 were directional in part but with subsequent return toward an earlier state. Thus, this review of temporal trajectories suggests a wide variety of community responses to manipulation, natural disturbance, or mere passing of time, but more than half showed saltatory change(s), and the majority showed a tendency to return to a former state if displaced, supporting the earlier concepts of Lewontin (1969) and May (1973) of Oecologia b c d e f Saltatory Gradual a Non-directional Directional Directional with return Fig. 1 Hypothetical trajectories of temporal change in communities, depicting temporal movement of a community through multivariate species-space, as might be analyzed using non-metric multidimensional scaling (NMDS), correspondence analysis, or detrended correspondence analysis plots. The framework depicts gradual versus saltatory change crossed with non-directional (idiosyncratic), directional, or directional change with return. Saltatory changes could result from stochastic events like floods or droughts, whereas return toward a previous community state might result from deterministic processes. Trajectories include a gradual, non-directional; b gradual, directional; c gradual, directional with return; d saltatory, nondirectional; e saltatory, directional; f saltatory, directional with return. The black dot represents the first of 15 sequential surveys of a hypothetical community communities lying within some probabilistic ‘‘cloud of points,’’ and Collins’ (2000) concept of communities in general showing ‘‘loose equilibrium.’’ It is in this light that we assess the Brier Creek fish community, over four decades, to test applicability of our framework in a system in which some of the most extraordinary, and repeated, disturbances (flood and drought) on record have occurred. To test predictions of any theoretical constructs about communities, long-term empirical studies are extremely valuable (Magurran et al. 2010). Long-term studies can detect patterns that only develop across generations of organisms. Connell and Sousa (1983) emphasized that studies of community dynamics should be long enough to allow at least one complete turnover of all individuals in the original community. Long-term studies are also more likely to include natural disturbances of differing kinds or intensities (Bêche and Resh 2007) such as unpredictable, rare, catastrophic disturbances like extreme floods (Matthews 1986; Thibault and Brown 2008), extraordinary droughts (Lake 2011), or hurricanes (Lugo et al. 2000; Willig et al. 2011; Geheber and Piller 2012) that can be major agents of community change or have non-linear effects (Brown and Ernest 2002; Turner et al. 2003). Longterm studies can help identify the relative importance of different community-organizing processes (Grossman and Sabo 2010). Numerous recent studies at the scale of multiple decades (20 years or longer) are on communities including phytoplankton, zooplankton, corals, stream invertebrates, intertidal or benthic marine communities, fishes, salamanders, small mammals and birds (Elliott 1990; Hairston and Wiley 1993; Cody and Smallwood 1996; Coppedge et al. 2001; Warwick et al. 2002; Eby et al. 2003; Paine and Trimble 2004; Wakeford et al. 2008; Gido et al. 2010; Magurran and Henderson 2010; Thibault et al. 2010). However, questions that still beg for generalization across long-term studies of communities include: 1. 2. 3. 4. What is the relative importance of ‘‘event-driven’’ versus gradual change (Mittlebach et al. 2006; Jentsch et al. 2007)? Do communities typically change states (Scheffer and Carpenter 2003) after some threshold is reached (Dodds et al. 2010) or after catastrophic disturbance (Carpenter et al. 2011)? Do communities follow long-term directional trajectories (Collins 2000; Muehlbauer et al. 2011) that can be related to species-specific life history or physiological traits? What are the effects of repeated disturbances over short periods of time? Here, we address the dynamics of the Brier Creek fish community over a span of 40 years, and test hypotheses about observed changes as related to disturbance. This is one of the longest available datasets for a stream fish community. During our study period, Brier Creek had three extraordinary disturbance events, including the worst erosive flood on record for the watershed and extreme droughts only 2 years apart, along with numerous other erosive floods and dry periods. We document variation in 123 Oecologia the fish community in 16 surveys from 1969 to 2008 and use 14 surveys we personally conducted from 1981 to 2008 to test hypotheses about drivers in the dynamics of the fish community. Thus this multi-decade data set provides the opportunity to: (1) assess long-term qualitative and quantitative variation in a real community; (2) test the hypothesis of more change than at random in response to disturbance events in general, or to events of extreme magnitude; and (3) test whether, after event-driven change, the community returned toward an earlier, ‘‘typical’’ condition (as opposed to remaining in an alternate state). We also evaluated mechanisms of the observed changes as related to life history or behavioral traits of individual species, or to changes in abundance of particular trophic groups (particularly for predators and potential prey), and compared the observed trajectory of the Brier Creek fish community to the hypothetical patterns in Fig. 1. Materials and methods Study area Brier Creek (33°N, 98°W) is a small, clear, gravel-bed stream, mostly with riffle-pool structure, draining 59.6 km2, with a main stem approximately 20 km long, in Marshall County, south-central Oklahoma, USA (Fig. S1, ESM2). The shallow headwaters are mostly in open pasture lands dominated by cattle grazing, whereas the lower main stem is characterized by deeper pools, incised in earthen banks several meters high and surrounded by riparian forest (ESM2). Flow is often interrupted in the headwaters during dry spells, but the lower main stem flows perennially except in the worst droughts. Brier Creek is a direct tributary of Lake Texoma, a large manmade reservoir impounded on the Red and Washita rivers in 1947. The watershed is entirely rural, with little change in land use since the initial fish survey in 1969 (Smith and Powell 1971; Matthews and Marsh-Matthews 2007). The region has hot summers and cold winters, with 97 cm average annual precipitation, and the Brier Creek watershed is characterized by a generally harsh, fluctuating environment (Ross et al. 1985; Matthews 1987). Brier Creek is prone to erosive floods, with rapid stage rises of 4.5 m or more, and peak calculated discharges as much as 55 m3/s (Harvey 1987; Power and Stewart 1987; Matthews et al. 1994; Wesner 2011), and velocity approaching 2 m/s (W. J. M., field notes). These floods move the stream bed, scour or deposit gravel to form or fill pools, and undercut stream banks, causing logs or whole trees to be swept downstream (Harvey 1987; Power and Stewart 1987). The creek also has a history of extreme droughts, with fish crowded into tiny isolated pools or 123 eliminated from headwater sites (Matthews 1987; Matthews and Marsh-Matthews 2003, 2007, 2010). Eight of the 13 intervals between our 1981–2008 surveys and the interval before the 1981 survey included severe to extreme events, including erosive floods, droughts, or both (ESM2). We subjectively classified four of the events as ‘‘extreme’’ relative to all others based on climate records and our own field observations (ESM2). Extreme events included: (1) drought in summer 1980 (Palmer Z short-term drought index = -3.90, http:// climate.ok.gov) with extremely high temperatures, resulting in direct heat death of some fishes (Matthews et al. 1982; Ross et al. 1985); (2) a massive flood in October 1981 due to 66 cm of rain in 7 days, with 26 cm in 3 day; (3) the worst drought on record in summer 1998 for SouthCentral Oklahoma Climate Division (Palmer Z = -4.42); and (4) a locally extreme drought in summer 2000, with no measurable rain in Marshall County in August (MarshMatthews and Matthews 2010). Brier Creek is a good model for other small streams. Evidence from collections included in this paper and other ancillary sampling (W. J. M., E. M. M., unpublished data) indicates that the system is open to immigration of fishes from the reservoir (ESM3), and that temporal changes in the fish community are similar in magnitude to changes in other streams in southern Oklahoma (ESM3). Thus, Brier Creek is a system that may relate well to other small streams in rural or agricultural regions of the southern United States. And, due to extensive reservoir building in the latter half of the 20th century in the United States (Baxter 1977) and worldwide (Nilsson and Berggren 2000), many small streams are now direct tributaries to man-made reservoirs (e.g., Falke and Gido 2006), so findings from Brier Creek may be pertinent to many other streams that flow directly into large reservoirs. Fish sampling: history and technique History of all surveys, details of sampling, and validation of sampling methods are in ESM4. Brier Creek has a long history of fish community surveys (Smith and Powell 1971; Ross et al. 1985; Matthews et al. 1988; Matthews and Marsh-Matthews 2006b) and ecological studies of fishes (Power and Matthews 1983; Gelwick and Matthews 1992), which provide detailed descriptions of the watershed or floods and droughts. Brier Creek is characterized by native fishes that are tolerant of physicochemical stressors (Matthews 1987). The earliest known, but unpublished, fish collection in Brier Creek was at one downstream site by Carl Riggs in July 1950 (C. Riggs, field note R50-9, Sam Noble Oklahoma Museum of Natural History). The first comprehensive fish survey of the watershed was by Smith and Powell (1971), in summer 1969 at six fixed sites. In Oecologia 1976 Echelle and class (W. J. M. participated) surveyed fish at five of Smith and Powell’s sites, and at one new headwater site (Fig. S1, ESM1). We (the present authors) sampled those six sites in 14 summers from 1981 to 2008, with the exception that in 1988 the uppermost site was dry, so only five sites were sampled. The 1981–2008 surveys were directed by W. J. M. with the exception of 1986 and 1995, and there was cross-participation of all authors in various surveys (Table 1). Sampled stream reaches were 200- to 500-m (mean = 360 m) long (site descriptions in ESM2). Our goal was to sample all species in proportion to their abundance, in all available microhabitats such as open pools, undercut banks, root wads. woody debris, and vegetation. We used seines 4.6 m long 9 1.2 m deep with 4.5mm mesh in pools, with shorter seines of similar mesh (to 1.8 m long) for kick sets in flowing riffles or in narrow headwaters channels where shorter seines were more efficient. Fish were preserved for enumeration in the laboratory with the exception that large-bodied adults were often identified, recorded and released. Our 1981–2008 samples are archived in the Department of Ichthyology, Sam Noble Oklahoma Museum of Natural History. We followed Matthews (1998, as modified from numerous sources) to classify Brier Creek species into trophic groups based on their primary diet as adults (Table 1), to compare temporal changes among groups. Data analyses Data were pooled across the six fixed sites to form a composite community data set for Brier Creek in each survey year (Table 1). Habitats in Brier Creek range from the small, harsh headwaters sites to the larger, lower main stem (Matthews 1987), resulting in distinct longitudinal differences in fish species distributions (Smith and Powell 1971; Ross et al. 1985; Matthews 1987). However, the focus here is on the ‘‘big picture’’ of long-term dynamics of the total fish community of the watershed, and detailed analysis of longitudinal patterns or site-specific temporal changes will be the subject of future papers, as additional long-term data are gathered. For the composite survey data, we followed Ross et al. (1985) and calculated mean total abundance (Table 1) of each species across seven sampling dates in 1969 by Smith and Powell (1971), and across two samples in June and July 1981 by W. J. M. From 1969 to 2008 a total of 32 species was detected (Table 1). We used Jaccard’s index (JI) to estimate species turnover among surveys. For multivariate analyses we omitted species that occurred only once, or totaled five or fewer individuals across all surveys (Table 1). We limited the multivariate analyses on the 23 remaining species to the surveys we directed from 1981 to 2008, for which we have personal information on antecedent environmental events. For multivariate analyses, we converted abundances to log10(x ? 1), improving linearity among some species pairs and lessening the potential influence of highly abundant species. With log-transformed data, we initially compared five resemblance metrics and three ordination methods that are commonly used in community ecology (ESM5). The multivariate analysis in the ‘‘Results’’ is based on the Bray-Curtis distance (BCD) among surveys followed by non-metric multidimensional scaling (NMDS). We also used BCD to quantify changes in the fish community between individual surveys. BCD was not autocorrelated between consecutive surveys [Wessa 2012; free statistics software version 1.1.23-r7; autocorrelation at lag 1, with white noise time series: ACF (k) = 0.259, P = 0.18]. To provide comparative ordination methods, we also carried out correspondence analysis (CA), and detrended correspondence analysis (DCA), which are commonly used in community ecology, on the 1981–2008 data. Results of CA and DCA were similar to NMDS with respect to trajectories, temporal trends, and effects of drought, so biplots of CA and DCA are shown only in ESM6. Calculations of BCD and all ordinations were by PCORD version 6. For NMDS of the triangular BCD matrix we first used the step down option of PC-ORD from six to two axes, without the autopilot option, and used a scree plot to determine optimal stress versus number of axes. The best solution was a two-dimensional solution, and we used the weighted averages option in PC-ORD to position species centroids on the two NMDS axes. We used the first final two-dimensional run of the NMDS for results, but we also re-ran the two-dimensional NMDS several additional times as recommended by McCune and Grace (2002). Results were similar each time, so the NMDS should be a stable solution, not affected by local minima (McCune and Grace 2002). Following the approach of Hughes (1990) we used a clustering classification analysis to objectively delineate post hoc groups of surveys on the NMDS biplot. For this we did a unweighted pair group method with arithmetic mean (UPGMA) cluster analyses based on BCD between all pairs of surveys, in PC-ORD. To determine if some surveys were more extreme on the NMDS biplot than was likely at random, or if BCD between some consecutive surveys were larger than random, we used the Monte Carlo algorithm of Schaefer et al. (2005) (program obtained from Ecological Archives A015052-S1), as detailed in ESM7. To test for evidence that events caused saltatory change, we compared BCD to numbers of events (drought, flood, or both; ESM2) by Spearman rank correlation. We also used Mann–Whitney tests to compare BCD between: (1) intervals that included ‘‘events’’ (of either kind) versus those 123 Trophic group BO A H IO IO IO IO IO IO IO BO BO BI BI O O P IO IO IO IO P P P P IO IO IO M P P BI BI Scientific name Cyprinus carpioc Campostoma anomalum 123 Ctenopharyngodon idellac Cyprinella lutrensis Cyprinella venusta Notemigonus crysoleucas Notropis boops Notropis stramineus Pimephales promelas Pimephales vigilax Carpiodes carpioc Ictiobus bubalusc Minytrema melanops Moxostoma erythrurum Ameiurus melas Ameiurus natalis Ictalurus punctatusc Gambusia affinis Labidesthes sicculusc Menidia beryllinac Fundulus notatus Micropterus punctulatus Micropterus salmoides Lepomis cyanellus Lepomis gulosusc Lepomis humilis Lepomis macrochirus Lepomis megalotis Lepomis microlophus Pomoxis annularisc Pomoxis nigromaculatusc Etheostoma spectabile Percina macrolepida 2 63 0 1 0 26 4 0 1 6 5 4 10 0 3 0 0 5 0 0 0 0 0 2 6 14 0 0 2 34 0 14 0 Riggs 1950a Site6 1 61 0 0 1 141 16 28 0 45 6 19 64 1 2 1 0 8 4 0 0 0 1 19 57 0 669 2 3 124 0 68 1 Smith and Powell 1969b Table 1 Species collected in Brier Creek, Marshall County, Oklahoma, USA 0 86 0 0 0 44 9 22 0 54 2 1 25 0 0 102 0 1 8 2 0 0 0 3 0 0 233 1 35 9 0 205 0 Echelle 1976 WJM 3 166 0 1 23 56 67 65 0 125 45 0 24 0 0 19 1 2 0 0 1 0 1 10 19 0 82 26 73 158 0 165 0 1981 WJM 65 160 1 0 6 216 106 41 0 665 102 1 19 0 0 4 0 22 7 0 3 0 1 7 5 4 424 13 42 129 0 600 0 1985 WJM, FG 4 12 0 0 7 60 61 7 0 155 47 0 41 0 0 0 0 0 15 0 0 0 0 2 0 0 901 4 43 232 0 218 0 1986 RCC 9 1,193 0 0 15 190 61 28 0 126 471 10 137 0 0 0 0 9 8 10 2 0 1 12 0 6 184 1 34 119 0 2194 0 1988 WJM 2 327 0 1 23 303 94 17 0 535 16 20 122 0 0 14 0 3 5 4 0 0 1 22 0 1 1,114 1 13 22 0 228 0 1991 WJM, FG 0 122 0 0 34 197 191 15 0 167 40 10 53 0 0 0 0 4 26 1 0 0 0 24 0 8 405 2 72 41 0 556 0 1993 WJM, RCC, FG Oecologia 0 0 0 0 0 0 0 1 0 0 0 1,628 3,408 0 61 0 0 7 414 156 0 0 217 42 21 703 0 0 248 0 5 4 2 0 0 0 11 0 1 1,399 0 8 33 0 75 0 1996 WJM, RCC, FG 1,822 2 472 0 0 5 311 64 1 0 34 405 8 63 0 0 13 0 6 1 3 3 0 0 0 0 0 317 1 0 0 3 110 0 1999 WJM 4,400 2 588 0 1 11 76 54 136 0 457 460 84 15 0 0 13 0 35 2 291 238 0 0 2 0 4 508 11 0 8 0 1,397 1 2001 WJM, EMM 3,136 2 544 0 0 12 179 72 19 0 427 64 122 32 0 0 0 0 15 20 89 37 0 0 2 30 13 162 7 0 1 0 1,272 0 2002 WJM, EMM. 3,856 16 399 0 0 30 451 143 3 0 559 161 27 242 0 0 15 0 5 19 28 1 0 0 0 1 119 911 23 16 7 0 678 0 2004 WJM, EMM 3,403 0 67 0 0 23 166 95 10 0 523 117 56 97 0 0 0 0 4 0 20 4 2 0 0 7 10 383 23 28 71 0 1,693 0 2008 WJM, EMM c b a Omitted from multivariate analyses Smith and Powell (1971) C. Riggs, field note R50-9, Sam Noble Oklahoma Museum of Natural History BO Benthic omnivore, A Algivore, H herbivore (on macrophytes), IO insectivore/omnivore, BI benthic insectivore, O omnivore, P piscivore, M molluscivore Initials following collection year indicate which of the authors participated in that collection 2,279 5 137 0 0 225 3 62 106 195 169 120 43 41 12 51 118 10 13 0 9 0 0 0 0 34 0 0 0 0 1 1 2 7 24 0 0 0 2 13 11 856 0 0 35 72 63 523 0 94 22 139 0 1995 RCC, FG 0 667 0 1994 WJM, RCC, FG Table 1 continued 11 16 1 3 15 16 16 14 16 16 14 16 1 1 11 2 14 14 11 8 1 5 13 6 11 16 13 13 15 1 16 2 Occurrences 1969–2008 Oecologia 123 Oecologia Results Overall variation in the community In 1950, Riggs recorded 18 species at one Brier Creek site (Table 1), of which we collected 16 from 1981 to 2008. The two species in Rigg’s sample we did not find from 1981 to 2008 were brook silversides (Labidesthes sicculus), which Riggs in 1950 and Smith and Powell (1971) in 1969 detected in very low numbers, and warmouth (Lepomis gulosus), which we did not collect from 1981 to 2008. However, in additional sampling at two sites after 2008 we (W. J. M., E. M. M., unpublished data) subsequently found several warmouth. As another indicator of the low turnover of species across time in Brier Creek, 28 species were detected in sampling six sites throughout the watershed by Riggs, Smith and Powell, or Echelle from 1950 to 1976, or in our surveys in the 2000s (Table 1), with 24 shared between the early surveys and ours of the 2000s (JI = 0.887). In our 1981 survey we detected 22 species, and found 20 of them again in the 2000s (JI = 0.952). The two species from 1981 we did not find in the 2000s were river carpsucker (Carpiodes carpio) and channel catfish (Ictalurus punctatus) for which we found only one each in 1981. Eight species that occurred in all 16 of the system-wide surveys from 1969 to 2008, and nine other species that were detected in most (13–15) surveys (Table 1) comprised a core of 17 species in Brier Creek. Six other species were 123 detected in six to 11 surveys, for a total of 23 species common in the Brier Creek community. Nine species were detected only rarely (Table 1), including large-bodied species and two silversides that were likely strays from Lake Texoma, and one exotic (grass carp, Ctenopharyngodon idella, that is frequently stocked in ponds for weed control). One species (sand shiner, Notropis stramineus) not found in our surveys until 1985, became established and occurred in ten of 12 subsequent surveys (Table 1). No abundant species in Brier Creek disappeared completely during the study, although several showed sharp declines (Table 1). The most common species varied markedly in abundance in various surveys, but not synchronously (Table 1). The most abundant trophic groups were water column insectivore-omnivores (minnows, topminnows, smallmouthed Lepomis sunfishes, and western mosquitofish, Gambusia affinis), and piscivores (including largemouth bass, Micropterus salmoides, and spotted bass, Micropterus punctulatus, and large-mouthed Lepomis sunfishes) (Table 1). From 1969 to 2008 the percentage of species that are piscivores as adults increased (Pearson r of piscivores vs. years = 0.505, P = 0.046), and water column insectivores and insectivore-omnivores decreased (r = -0.462, P = 0.072), resulting in a strong negative relationship (Pearson r = -0.630, P = 0.009) between these trophic groups (Fig. 2). Community trajectory in multivariate space We focus on the position of individual surveys and the temporal trajectory of the community in the NMDS biplot (Fig. 3a) to summarize long-term trends in Brier Creek. Our 1981 survey, which was located at the far left on axis 1 100 Insectivore-Omnivores (%) that did not, (2) intervals that did or did not include flood, and (3) intervals that did or did not include drought. If community change is directional over time, biplots should exhibit a trend for progressive divergence of surveys from the initial state. On the NMDS biplot we counted the number of movements away from versus back in the direction of the community in our first (1981) survey. We also followed Hughes (1990) and used the angles of movements between consecutive surveys in the NMDS biplot to ask if, in each step, the community continued to move further away from the previous position, or back toward it. If the angle of the trajectory from time 1 to 2 to 3 is obtuse ([90°) then the community is continuing to move further away from the point represented by time 1, whereas acute angles (\90°) represent movement back toward time 1, not contributing to an overall directional trajectory. We also compared each survey to our initial survey in 1981, and tested for increases in BCD with years since the initial survey by linear regression, followed by a runs test (PASW Statistics 18, 2007) of increasing versus decreasing BCD values relative to 1981 to identify trends during any particular time periods. 80 60 40 20 0 0 5 10 15 20 25 30 35 Piscivores (%) Fig. 2 Percentage of insectivore–omnivores versus percentage of piscivores in Brier Creek in each survey of 1969–2008 Oecologia a 1.5 2002 1.0 2001 2008 0.5 1981 1985 1988 2004 0.0 -0.5 1999 1994 1993 1991 1986 -1.0 1996 1995 NMDS 2 of the NMDS (Fig. 3a), followed an unusually hot, dry summer in 1980 (Ross et al. 1985; Online Resource 1). The 1985 survey moved toward the middle of the biplot, but not with an unusually large BCD, even though the most extreme flood (October 1981) and other dry periods and floods were in that interval (ESM2). From 1981 up to and including 1994, surveys were in relatively limited space to the left in the biplot (Fig. 3a). Then in 1995 and 1996 the trajectory moved downward on axis 2. (Note that axes in NMDS biplots are of equal importance, thus movement in any direction on the biplot can be considered equally important, biologically.) Between the 1996 and 1999 surveys, the worst drought to that date for Marshall County occurred (in 1998; Matthews and Marsh-Matthews 2006b), and the 1999 survey was markedly displaced to the right side of the NMDS biplot. A second exceptional drought occurred in summer-fall 2000 (Matthews and Marsh-Matthews 2006b, 2010), and the survey in 2001 showed another large displacement in NMDS space, upward on axis 2. The movements of surveys in NMDS space in 1999 and in 2001, after two extreme droughts in close succession (1998 and 2000), were the largest for any intervals between surveys (Fig. 3a), and these intervals had the two largest BCD values (0.245 and 0.242, respectively) for any intervals between surveys. Then, from 2002 through 2008 the community moved back toward a long-term average condition. UPGMA clustering (ESM6) of the surveys based on BCD values reinforced these interpretations by showing two distinct clusters at a BCD of 0.27 that included: (1) 1999, 2001, and 2002; and (2) all other surveys, including those in 2004 and 2008. But if a cutoff for clusters is placed at approximately BCD = 0.21 in the UPGMA tree (ESM6), five subclusters can be identified, with 1981 to 1986 as one subcluster; 1995 and 2001 each as a sole member of a separate subcluster; 2001 and 2002 as a subcluster; and, importantly, the surveys of 2004 and 2008 occurring in a subcluster with most of the other years in the middle of the NMDS plot. In other words, the UPGMA clustering (ESM6), whether we use a BCD cutoff of 0.21 (giving five subclusters) or 0.27 (giving two major clusters), shows the years 2004 and 2008, subsequent to the two extreme droughts of 1998 and 2000, to have moved back toward a typical Brier Creek community structure, i.e., closer to the middle of NMDS space (Fig. 3a). Monte Carlo simulations showed that three of the annual surveys were more different from the long-term average community than was likely at random (1986, P = 0.004; 1995, P = 0.003; 1999, P = 0.003), and a fourth survey (1996) was marginally different at P = 0.09. Monte Carlo simulations starting with real abundances for 1996 and, separately for 1999, showed that the BCD from 1996 to 1999 was significantly larger than at random (P = 0.04), and the BCD from 1999 to 2001 differed from random at -1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 1.5 2.0 b 1.0 MM PP NC LH PM 0.5 0.0 CL CV ME AN MP GA PV -0.5 -1.0 -1.5 -1.5 -1.0 -0.5 0.0 0.5 1.0 1.5 2.0 NMDS 1 Fig. 3 NMDS, based on Bray-Curtis distances, for Brier Creek surveys from 1981 to 2008, based on 23 species, with a survey scores indicated on axes 1 and 2, and b species overlaid on the same NMDS axes. Of the 23 species, 11 formed a highly overlapping cluster in the center of the NMDS plot, which are not individually identified in b. Species outside this core are indicated as follows: Cyprinella lutrensis (CL), Cyprinella venusta (CV), Notemigonus crysoleucas (NC), Pimephales promelas (PP), Pimephales vigilax (PV), Minytrema melanops (MM), Moxostoma erythrurum (ME), Ameiurus natalis (AN), Gambusia affinis (GA), Micropterus punctulatus (MP), Lepomis humilis (LH), Percina macrolepida(PM). Species in the core are identified in Fig. S10 (ESM) P = 0.09. The difference between surveys in 1996 and 2001 (which spanned the two severe droughts), was greater than the difference for any single interval, with BCD = 0.317, and a Monte Carlo simulation beginning with the 1996 data showed that the difference between 1996 and 2001 was much greater (P \ 0.001) than would have occurred by random fluctuations in species abundances. The Brier Creek NMDS biplot (Fig. 3a), judged by the same criteria we used for the 71 trajectories we classified by our hypothetical framework (Fig. 1; Online Resource 1), showed two (or possibly three) intervals with saltatory change (1986–1988, 1996–1999, and 1999–2001), and each of these intervals also had a large BCD. Each of these 123 Oecologia intervals included a severe drought (1996–1999, 1999–2001) or was a survey made during a severe dry period (1988). We also saw evidence of the trajectory after 2001 returning back toward an earlier state, e.g., toward the center of the biplot and/or toward the first survey in 1981, so we judged the overall pattern to show ‘‘return.’’ Thus, we classified Brier Creek as having ‘‘saltatory change, followed by return,’’ most nearly fitting hypothetical pattern F in Fig. 1. a Influence of individual species on multivariate analyses Testing for event-driven change and directional community trajectory If change is gradual, not event driven, differences among surveys could be a simple effect of ‘‘time.’’ But there was no correlation between BCD and numbers of years between surveys (Spearman’s q = 0.083, P = 0.786), and no significant correlation between BCD and number of events in an interval (Spearman’s q = 0.101, P = 0.744). Viewed by occurrence of different type(s) of events (regardless of number in an interval), there was a trend for more change 123 b Bray-Curtis distance Notable trends that relate to positions of the surveys in the NMDS biplot (Fig. 3a) included: maxima for western mosquitofish in 1976 and 1996; major increases in largemouth bass, golden redhorse (Moxostoma erythrurum), spotted sucker (Minytrema melanops), and orangethroat darter (Etheostoma spectabile), following extreme droughts in 1998 or 2000; and declines in red shiner (Cyprinella lutrensis), and blacktail shiner (Cyprinella venusta) in recent surveys (Table 1). The overlay of species weighted averages on the NMDS axes (Fig. 3b; Fig. S10 in ESM6) suggested that movement of the 1995 survey toward the lower left in the biplot coincided with a decrease in numbers of central stonerollers (Campostoma anomalum), low numbers of black striped topminnows (Fundulus notatus), and relatively high numbers of red shiners and blacktail shiners. Movement of the 1996 survey toward the right on axis 1 coincided with the largest numbers of mosquitofish and topminnows in any of our surveys (Table 1). In 1999, following the extreme drought of 1998, the large move of the community to the right and upward on the NMDS biplot coincided with a large increase in largemouth bass and loss of red shiners and blacktail shiners (Table 1). Then, after the severe drought in 2000, the surveys in 2001 and 2002 were in the upper part of NMDS axis 2 (Fig. 3a), reflecting increases in the two suckers: golden redhorse and spotted sucker (Table 1). But by 2004 and 2008 abundances of the suckers and bass decreased, red and blacktail shiners were again found (Table 1), and the community moved back toward the middle of the biplot. c Fig. 4 Boxplots comparing Bray-Curtis distances between consecutive surveys in intervals without (NO) and with (YES) a flood and drought events, b floods, and c droughts (larger BCD) in intervals with either flood or drought relative to intervals with no events (Fig. 4a); no effect of floods alone (Fig. 4b); but a significant effect of drought alone (Fig. 4c) relative to all intervals lacking drought (Mann–Whitney U = 7.00, P = 0.05, MedCalc version 11.2.1). In addition, the largest BCD values corresponded to two intervals (1996–1999, 1999–2001) with the most extreme droughts during our study period. A runs test (PASW statistics) of the increase or decrease of Bray–Curtis distances between the 1981 survey and all surveys 1985–2008 (Fig. 5) was non-significant (P = 0.999), reinforcing the finding that there was no Oecologia 0.32 Bray-Curtis distance relative to 1981 0.30 0.28 0.26 0.24 0.22 0.20 0.18 0.16 0 5 10 15 20 25 30 Years since 1981 Fig. 5 Bray-Curtis distances comparing each survey to the survey in 1981, versus number of years since 1981 overall directional trend away from the initial community state. BCD versus years since 1981 (Fig. 5) suggested a general trend away from the initial survey until the period 1999–2002, followed by a distinct reversal in 2004 and 2008, with the BCD for those intervals relative to 1981 becoming smaller, indicating a return toward an average community state. In the Brier Creek NMDS trajectory (Fig. 3a) there were eight acute angles, compared to four obtuse angles, indicating a lack of overall directionality. In the biplot six surveys (not including 1985, which could only move away from the starting point of 1981) moved further away from the 1981 survey, and six moved closer to 1981, also indicating no overall directional displacement of the community. Discussion Long-term variation in Brier Creek Qualitative changes in the Brier Creek community were relatively small over almost 60 years, since the first known collection in 1950. Core species (e.g., Magurran and Henderson 2010) were nearly always present from 1969 to 2008. Qualitative variation among surveys was mostly due to rare, non-persistent transients presumed from Lake Texoma. Only one new species became established from 1981 to 2008, and no species that was common in the earlier surveys disappeared completely. Most species that were detected in early samples remained present in the watershed in recent surveys, indicating substantial qualitative stability in fish community composition, or high ‘‘persistence’’ sensu Connell and Sousa (1983). Quantitatively, individual fish species in Brier Creek showed substantial variation in abundance but interspecific population fluctuations were asynchronous and most species tended to return toward average values after years of peak abundance, varying around their mean, as did fishes in Magurran and Henderson (2010). There were noteworthy changes in abundance between some trophic groups, e.g., an increase in piscivores coincided with a decline in water column insectivorous minnows. But changes in these trophic groups did not result in long-term change in community composition from the earlier state to one persistently different. We conclude that the Brier Creek fish community trajectory is closest to our hypothetical pattern in Fig. 1f, i.e., that the community did show saltatory change after two extreme droughts, but transiently, with return toward an average community state. This return toward a more average state suggested long-term stability as defined by Bêche and Resh (2007) or a loose equilibrium (Collins 2000). It seems noteworthy that the two extreme droughts, with only one wetter year in between, caused large, nonrandom displacement of the Brier Creek fish community in multivariate space. And effects of individual droughts may be idiosyncratic: our surveys in 1985, 1988, and 2008, each following or during a drought period, showed no consistent amount or direction of movement of the community in NMDS space. We suspect that the two temporally close, extreme droughts of 1998 and 2000 were unique in their degree of impact on the Brier Creek community. In response to extreme events, other stream fish communities have shown many different responses, including resistance to change (Meffe and Minckley 1987), rapid recovery to a pre-event state (Matthews 1986; Franssen et al. 2006), or change to a persistent altered structure (Strange et al. 1993). Effects may differ among taxonomic or ecological groups (Matthews et al. 1994; Marsh-Matthews and Matthews 2010) or among individual species (Wesner 2011). Long-term data by Magurran and Henderson (2010) for a complex estuarine fish community suggest a similar pattern of considerable variation in species abundances or community properties from year to year, yet stability in the overall community or in its core species (i.e., no directional change in structure) over a span of 30 years. Other long-term studies of fishes have shown that several decades of change may be directional, but at times communities may sharply reverse their trajectories, and return toward an earlier state (Eby et al. 2003; Pyron et al. 2006). Multivariate trajectories of community change for other taxa ranging from macroinvertebrates to woody plants have shown marked displacement following experimental treatments or disturbances, followed by return toward pre-disturbance composition (Gardner and Wear 2006; Muehlbauer et al. 2011), and our assessment of 71 trajectories across numerous studies (ESM1) indicated that such patterns are common. But there is not yet enough evidence to allow a general consensus that changes in 123 Oecologia stream fish communities (or communities in general) are typically gradual, event driven, or idiosyncratic, thus, as Jackson et al. (2001) indicated, the need remains for longterm data on more communities of all kinds. There have, however, been a substantial number of studies of freshwater fish communities spanning decades (Eby et al. 2003; Beugly and Pyron 2010; Gido et al. 2010; Stefferud et al. 2011; Penczak 2011) that underscore the value of including sufficient time for the expression of effects of events, whether natural or anthropogenic. And events during the last decade of our own surveys support the importance of long-term studies of communities. If our surveys had ended in 1996, before the two extreme droughts in 1998 and 2000, we might have concluded that the Brier Creek fish community was characterized by gradual, directional change away from its state in 1981, and only minimally affected by disturbance events. Bêche and Resh (2007) provided a similar cautionary note about potentially false conclusions from short-term data. Our continued surveys in the last decade allowed us to document responses to the two extreme droughts, and reach a very different conclusion: that the community changed rather gradually and somewhat directionally for approximately 15 years, until punctuated by event-driven changes in trajectory, but after which the community reversed back toward a more typical pre-disturbance condition. Without the long-term data we would have completely overlooked this important difference in dynamics of the system. Mechanisms driving change and recovery Hydrology is critical in stream systems (Sabo et al. 2010), but fishes in Brier Creek (Matthews et al. 1994; Wesner 2011) or other streams (Meffe and Minckley 1987; Matthews 1986, 1998) may be less affected by flood than drought, as adults in erosive floods typically find refuge from strong currents. The great flood of October 1981 was one of three ‘‘extreme’’ events in our study, but there was little signal of its negative effects as of the next survey in 1985. And flooding can clean substrates of silts and expose bedrock or gravel substrates, potentially favoring fish that are egg attachers or gravel nesters. Floods in Brier Creek can decimate fish larvae (Harvey 1987), but there is no evidence that adults are washed out of the system. During erosive flooding in Brier Creek adult fish typical of pool or riffle habitats use low-velocity microhabitats along stream edges or in flooded woods (W. J. M. field notes). Franssen et al. (2006) and Wesner (2011) suggested that erosive floods may actually facilitate recolonization of fish. In our study, drought caused more changes in the fish community than floods. Drought or dry periods can have severe effects in both terrestrial (Frank and McNaughton 1992; Yahner 1992; Zeng and Qian 2005) and aquatic 123 ecosystems (Sabo and Post 2008; Sabo et al. 2010; Lake 2011). Droughts cause direct mortality of fish from crowding in isolated pools, where water quality declines and small fish become prey for larger species (Matthews and Marsh-Matthews 2007), or result in many indirect or residual effects (Matthews and Marsh-Matthews 2003). But after drought, fish that survive may rapidly recolonize rewatered reaches (Franssen et al. 2006), and reproduce successfully (Matthews 1987). Most common species in Brier Creek are tolerant of high temperatures or low oxygen, common in isolated pools during drought (Matthews 1998). Our overall evidence, like that of trajectories in Magalhães et al. (2007), suggest that after even severe drought, fish communities will tend to recover over a period of years back toward their earlier configurations. However, our evidence suggests that consecutive severe droughts (e.g., a second drought before the community has recovered from the first) may intensify the effect on a fish community beyond that of any single drought. Differences among species in ability to resist stressors like high temperature and low oxygen (Matthews 1987) can result in differential survival in drought (Marsh-Matthews and Matthews 2010). After drought, survivors may rapidly recover to body condition equal to (or greater than) that of congeners not subjected to drought (Marsh-Matthews and Matthews 2010). Orangethroat darters that survived an experimental drought showed substantial postdrought recovery of physical condition (Marsh-Matthews and Matthews 2010), and this species showed large population increases in Brier Creek in 1999 and 2000 after the two most severe droughts, with the most young-of-year darters we have ever observed in the system. There was also a major increase in numbers of youngof-year largemouth bass in 1999 and 2001, and a dramatic increase in young suckers in 2001 after the second extreme drought. The mechanisms underlying these reproductive bursts are not known, but the suckers are large-bodied, highly mobile species that might lack suitable refugia in Brier Creek during extreme drought, and adults might have migrated downstream to permanent water in or near the reservoir. Adult suckers migrate upstream to spawn, and might have done so in 2001, following the 2000 drought. One possible mechanism that could have enhanced reproduction by the suckers as well as bass is that several insectivorous minnow species that also eat fish eggs or larvae were not detected in 1999 and were very scarce in 2001. The sharp decline in minnows also coincided with long-term increases in abundance of their potential predators (large sunfish and black bass), shown to have important effects on minnows in this system by Power and Matthews (1983) and Marsh-Matthews et al. (2011). Red shiners, blacktail shiners, and sand shiners all eat fish eggs (Surat 1979), and red shiners are aggressive predators of Oecologia sucker larvae (Karp and Tyus 1990) or other species (Gido et al. 1999). So, for the benthic spawning species suckers and bass, there might have been less predation pressure on developing eggs or larvae in the years following the droughts, when most minnows were absent or in very low numbers. However, in the long view of the community, the sharp peaks in suckers and bass due to increased production of young in the years after the 1998 or 2000 droughts were not sustained, and did not result in a permanent elevation in abundance of these species after 2001. The scenario above underscores the potential importance of the integration of biotic and abiotic factors and interspecific interactions. We consider long-term increases in piscivores in Brier Creek to be related to physical changes in the environments lower in the creek (Matthews and Marsh-Matthews 2007). If minnows declined due to increases in predators, the effects of drought, or both, and thus released gravel-spawning larger species (bass, suckers) from egg or larvae predation, resulting in better recruitment of the latter, this complex array of interactions of physical structure, drought-related stress, and species interactions, would be worthy of more experimentation or species-specific, trait-based modeling, in Brier Creek or other systems. We suspect that mechanisms related to individual species traits, such as high tolerance for thermal or oxygen stress (Matthews 1987), ability to survive during or recover from drought-related stresses (Marsh-Matthews and Matthews 2010), or seek out refuge habitats during flood or drought and then recolonize (Matthews 1987), all help to produce long-term stability in the community under the current climate and disturbance regime. We do know that the species best surviving drought in Brier Creek the early 1980s, and most successfully recolonizing and producing young in rewatered headwater reaches, were species with the greatest tolerance for low oxygen conditions (Matthews 1987). Conclusion Our findings suggest that the Brier Creek community since 1969 had tended toward deterministic regulation about a loosely stable (Collins 2000) equilibrium, with generally persistent (Bêche and Resh 2007) core species, little species turnover, and species abundances that tend to return toward average (Bêche and Resh 2007; Magurran and Henderson 2010) in spite of the transient impacts of some events. In recent evolutionary time the fish community in the dynamic environment of Brier Creek has been exposed to frequent disturbances or harsh physical conditions, and individual fish species are well adapted to cope with vicissitudes typical of the past (Matthews 1987). But if predictions about global climate change, and increased frequency of severe events (Sheffield et al. 2012) are correct, then they, and many other animal and plant communities, will in the future be subject to repeated, frequent episodes outside the range of previous evolutionary experience. From a conservation perspective, predictions indicate that the southwestern United States will become hotter and drier, with droughts more frequent and more severe (US Global Change Research Program; http://www.globalchange.gov). In other habitats like coastal regions, storms like hurricanes may become more severe or more frequent. Geheber and Piller (2012) clearly show in a 22-year data set the strong alteration of a community after hurricanes Katrina and Rita, only a month apart in 2005. To the extent that the response of the Brier Creek community to consecutive severe droughts also serves as a model, there should be concern that the future climate could push systems beyond limits from which even naturally hardy native communities may not recover (Matthews and Zimmerman 1990). Being attuned to the fact that sequences of events, like the repeated severe droughts in Brier Creek, may have synergistic effects that are more than a ‘‘sum of the parts,’’ may provide a stimulus to and focus for future field, experimental, or modeling studies of all kinds of aquatic and terrestrial communities. Acknowledgments We thank two anonymous reviewers and the editors for helpful suggestions that improved the manuscript. We thank C. L. Smith for his seminal research and for sharing data, A. Echelle for leading the 1976 survey, S. T. Ross for detailed analyses of surveys through 1981, and K. Hauger, C. Hargrave, A. Marsh, R. Marsh, S. M. Matthews, C. Deen, M. Walvoord, I. Camargo, M. Brooks, N. Franssen, J. Stewart, and P. Lienesch, and students at the University of Oklahoma Biological Station classes for assistance in the field. We thank J. F. Schaefer for consulting on use of the Monte Carlo simulation program. 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